Existence of solutions for a class of $p(x)$-curl systems arising in electromagnetism without (A-R) type conditions

Ghasem A. Afrouzi; Nguyen Thanh Chung; Z. Naghizadeh

doi:10.5556/j.tkjm.51.2020.2915

Existence of solutions for a class of $p(x)$-curl systems arising in electromagnetism without (A-R) type conditions

Authors

Ghasem A. Afrouzi Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar
Nguyen Thanh Chung Quang Binh University
Z. Naghizadeh Department of Mathematics, Faculty of Mathematical Sciences, University of Science and Technology of Mazan- daran

DOI:

https://doi.org/10.5556/j.tkjm.51.2020.2915

Keywords:

$p(x)$-curl operator, Electromagnetism, Mountain pass theorem, Fountain theorem

Abstract

In this paper, we study the existence and multiplicity of solutions for a class of of $p(x)$-curl systems arising in electromagnetism. Under suitable conditions on the nonlinearities which do not satisfy Ambrosetti-Rabinowitz type conditions, we obtain some existence and multiplicity results for the problem by using the mountain pass theorem and fountain theorem. Our main results in this paper complement and extend some earlier ones concerning the $p(x)$-curl operator in [4, 15].

Additional Files

Published

2020-10-01

How to Cite

Afrouzi, G. A., Chung, N. T., & Naghizadeh, Z. (2020). Existence of solutions for a class of $p(x)$-curl systems arising in electromagnetism without (A-R) type conditions. Tamkang Journal of Mathematics, 51(3), 187-200. https://doi.org/10.5556/j.tkjm.51.2020.2915